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  • Synergistic dual positive feedback loops established by molecular sequestration generate robust bimodal response Ophelia S. Venturellia, Hana El-Samadb,c, and Richard M. Murraya,1

    aDivision of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; and bDepartment of Biochemistry and Biophysics and cCalifornia Institute for Quantitative Biosciences, University of California, San Francisco, CA 94143

    Edited by Eric D. Siggia, The Rockefeller University, New York, NY, and approved September 7, 2012 (received for review July 16, 2012)

    Feedback loops are ubiquitous features of biological networks and can produce significant phenotypic heterogeneity, including a bi- modal distribution of gene expression across an isogenic cell population. In this work, a combination of experiments and compu- tationalmodelingwas used to explore the roles ofmultiple feedback loops in the bimodal, switch-like response of the Saccharomyces cer- evisiae galactose regulatory network. Here, we show that bistability underlies the observed bimodality, as opposed to stochastic effects, and that two unique positive feedback loops established by Gal1p and Gal3p, which both regulate network activity by molecular se- questration of Gal80p, induce this bimodality. Indeed, systematically scanning through different single andmultiple feedback loop knock- outs, we demonstrate that there is always a concentration regime that preserves the system’s bimodality, except for the double dele- tion of GAL1 and the GAL3 feedback loop, which exhibits a graded response for all conditions tested. The constitutive production rates of Gal1p and Gal3p operate as bifurcation parameters because var- iations in these rates can also abolish the system’s bimodal response. Our model indicates that this second loss of bistability ensues from the inactivation of the remaining feedback loop by the overex- pressed regulatory component. More broadly, we show that the sequestration binding affinity is a critical parameter that can tune the range of conditions for bistability in a circuit with positive feed- back established by molecular sequestration. In this system, two positive feedback loops can significantly enhance the region of bist- ability and the dynamic response time.

    gene-regulatory network | phenotypic variation | ultrasensitivity

    Cells are continuously faced with the challenge of sensing sig-nals in their environment and eliciting intracellular programs accordingly. Although changes in some environmental cues en- gender graded and proportional responses, others induce decisive action whereby a cell exhibits a binary (on or off) phenotypic change. In the latter case, amplification of phenotypic heteroge- neity may arise because single cells in a population make indi- vidual decisions based on their perception of the environmental stimulus, stochastic fluctuations in their molecular components, and memory of past conditions. This thresholded cellular re- sponse can manifest as a bimodal distribution in network activity across an isogenic cell population. Feedback regulation, which links the output of a circuit back

    to its input, expands the set of possible biological properties, including robustness to uncertainty (1), and can produce single- cell phenotypic heterogeneity in a uniform environment. Many features of individual positive and negative feedback loops have been elucidated, including enhancement of response time and reduction of gene expression noise by negative autoregulation, as well as signal amplification and bistability using positive autor- egulation (2–5). However, quantitative characterization of how multiple feedback pathways interact to regulate and fine-tune cellular decision-making presents many unresolved challenges. The galactose gene-regulatory network of Saccharomyces cer-

    evisiae (GAL) contains numerous feedback pathways. Isogenic single cells respond heterogeneously to a range of galactose

    concentrations, which manifests as a bimodal distribution of GAL gene expression across the cell population (6). In contrast to a graded response, in which the mean of a unimodal distribution is continuously adjusted as the input is modulated, variations in the concentration of galactose within a range shift the fraction of the cell population distributed between distinct metabolic states. Here, we focused on how the multiple feedback loops in the system shape this bimodal cellular decision-making strategy in response to galactose. The GAL circuit consists of regulatory machinery (Gal2p,

    Gal3p, Gal80p, and Gal4p) that dictates network activity and a set of enzymes required for metabolizing galactose (Gal1p, Gal7p, and Gal10p). In the absence of galactose, GAL genes are repressed due to the sequestration of the potent transcriptional activator Gal4p by the repressor Gal80p (7) (Fig. 1). In the presence of galactose, the membrane-bound permease trans- porter Gal2p significantly increases the rate of galactose uptake from the extracellular environment (8). Galactose and ATP-de- pendent activation of the signal transducer Gal3p lead to re- pression of Gal80p by sequestration, thus liberating Gal4p (9). The galactokinase Gal1p catalyzes the first step in galactose metabolism by phosphorylating galactose to form galactose 1- phosphate and has been shown to possess weak coinducing functionality (10). Galactose-dependent regulation of Gal2p, Gal3p, and Gal80p

    forms feedback loops because these proteins modulate network activity and are themselves transcriptionally regulated by Gal4p (11). Gal2p and Gal3p form positive feedback loops because up- regulation of their expression levels leads to an increase in pathway activity, whereas Gal80p reduces pathway activity and thus forms a negative feedback loop. In addition to Gal2p, Gal3p, and Gal80p, there is evidence to

    suggest that Gal1p has a regulatory role beyond its vital enzymatic function for growth on galactose (10, 12, 13). Gal1p is a close homolog of Gal3p and has been shown to interact with Gal80p with a weaker affinity than Gal3p (14, 15). Furthermore, a GAL3 deletion strain was shown to induce GAL gene expression at a significantly slower rate compared with WT, whereas cells with combined GAL1 and GAL3 deletions fail to activate their GAL pathway (16). A recent study demonstrated that cells initially grown in galactose and then transferred to glucose exhibit a faster induction response to a second galactose exposure than cells grown only in glucose, and that Gal1p was critical for this de- crease in response time (17). Finally, galactose induction was shown to consist of two stages, the first of which is dominated by

    Author contributions: O.S.V., H.E.-S., and R.M.M. designed research; O.S.V. performed research; O.S.V. analyzed data; and O.S.V., H.E.-S., and R.M.M. wrote the paper.

    The authors declare no conflict of interest.

    This article is a PNAS Direct Submission. 1To whom correspondence should be addressed. E-mail: murray@cds.caltech.edu.

    See Author Summary on page 19527 (volume 109, number 48).

    This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1211902109/-/DCSupplemental.

    E3324–E3333 | PNAS | Published online November 12, 2012 www.pnas.org/cgi/doi/10.1073/pnas.1211902109

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    mailto:murray@cds.caltech.edu http://www.pnas.org/content/109/48/E3324/1 http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1211902109/-/DCSupplemental http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1211902109/-/DCSupplemental www.pnas.org/cgi/doi/10.1073/pnas.1211902109

  • rapid association of Gal3p to Gal80p and a delayed second stage consisting of dominance of the Gal1p–Gal80p complex (18). In this paper, we use a combination of experimental meas-

    urements and computational modeling to demonstrate that the observed bimodality in the galactose metabolic pathway arises from an underlying bistability in the system and that this bi- modal response relies on the synergistic interplay of the GAL1 andGAL3 feedback loops. These central mediators have unique mechanistic roles in the GAL system because they both regulate circuit activity by competitive molecular sequestration of Gal80p. Although the bimodal response can be transformed into a graded response in the absence of the individual GAL1 and GAL3 feedback loops, this only occurs in a specific pa- rameter regime in which the constitutive production rates of Gal1p and Gal3p are greater than a threshold. A mathematical model recapitulates the experimental results and provides cru- cial insights about the roles of the autoregulatory loops on bistability. More broadly, a simple mathematical model is used to identify generalizable properties of positive feedback loops created by molecular sequestration that implement robust switch-like responses.

    Results History-Dependent Response Indicates That Bimodality Arises from Underlying Bistability and Gal1p Significantly Enhances Sensitivity to Galactose. The presence of bimodality does not necessarily imply bistability because a bimodal distribution can arise from stochastic effects (19–21). Hysteresis is a characteristic feature of bistability, in which the system jumps from one branch of stable steady states to a different branch of steady states as a parameter is continuously increased but jumps from the second branch of steady states back to the first branch at a different value of the parameter as it is continuously decreased. This behavior stems from a difference in the local stability of multiple stable equilibria. To determine if bimodality in the GAL system was linked to bistability, we checked for a history-dependent r

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